The global weak solutions to the Cauchy problem of the generalized Novikov equation

被引：4
|
作者：
Zhao, Yongye [1 ]
Li, Yongsheng [1 ]
Yan, Wei [2 ]
机构：
[1] S China Univ Technol, Dept Math, Guangzhou 510640, Guangdong, Peoples R China
[2] Henan Normal Univ, Coll Math & Informat Sci, Xinxiang 453007, Henan, Peoples R China
来源：
APPLICABLE ANALYSIS | 2015年 / 94卷 / 07期
关键词：
35G25; 35B30; 35Q53; 35A35; peaked solutions; global weak solutions; Cauchy problem; generalized Novikov equation; global strong solution; SHALLOW-WATER EQUATION; CAMASSA-HOLM EQUATION; WELL-POSEDNESS; PEAKON SOLUTIONS; WAVES; EXISTENCE; TRAJECTORIES; BREAKING;
D O I：
10.1080/00036811.2014.930826
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the Cauchy problem of the generalized Novikov equation. We first show that under suitable condition, the strong solution exists globally via some a priori estimates. Then, we prove the existence and uniqueness of global weak solutions by the approximation method. We also obtain the exact peaked solutions.
引用
收藏
页码：1334 / 1354
页数：21
相关论文
共 50 条
  • [1] Global weak solutions for a generalized Novikov equation
    Zheng, Rudong
    Yin, Zhaoyang
    [J]. MONATSHEFTE FUR MATHEMATIK, 2019, 188 (02): : 387 - 400
  • [2] Global weak solutions for a generalized Novikov equation
    Rudong Zheng
    Zhaoyang Yin
    [J]. Monatshefte für Mathematik, 2019, 188 : 387 - 400
  • [3] The Cauchy Problem on a Generalized Novikov Equation
    Li, Kunquan
    Shan, Meijing
    Xu, Chongbin
    Guo, Zhengguang
    [J]. BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2018, 41 (04) : 1859 - 1877
  • [4] The Cauchy Problem on a Generalized Novikov Equation
    Kunquan Li
    Meijing Shan
    Chongbin Xu
    Zhengguang Guo
    [J]. Bulletin of the Malaysian Mathematical Sciences Society, 2018, 41 : 1859 - 1877
  • [5] THE CAUCHY PROBLEM FOR A GENERALIZED NOVIKOV EQUATION
    Zheng, Rudong
    Yin, Zhaoyang
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2017, 37 (06) : 3503 - 3519
  • [6] GLOBAL ANALYTIC SOLUTIONS AND TRAVELING WAVE SOLUTIONS OF THE CAUCHY PROBLEM FOR THE NOVIKOV EQUATION
    Wu, Xinglong
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2018, 146 (04) : 1537 - 1550
  • [7] Global weak solutions to the Novikov equation
    Lai, Shaoyong
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2013, 265 (04) : 520 - 544
  • [8] Global weak solutions for the Novikov equation
    Wu, Xinglong
    Yin, Zhaoyang
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2011, 44 (05)
  • [9] On the Cauchy problem for the modified Novikov equation with peakon solutions
    Mi, Yongsheng
    Mu, Chunlai
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2013, 254 (03) : 961 - 982
  • [10] The Cauchy problem for the Novikov equation
    Yan, Wei
    Li, Yongsheng
    Zhang, Yimin
    [J]. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2013, 20 (03): : 1157 - 1169
12345